Occupation-selective photon-pair interactions in a flux-pumped SQUID resonator

In the quiet, super-cooled world of quantum computing, scientists often look to light trapped inside tiny electrical circuits to store information. These circuits act like high-quality rooms where microwave photons, the particles of light at radio frequencies, can bounce around for a long time without disappearing. Because these rooms are so good at holding onto energy, they offer a vast space to store complex data, far larger than what simple two-state switches can hold. However, to make this data useful, researchers must be able to manipulate it with precision. They need to perform specific operations on the light without disturbing the rest of the system. For years, the standard way to do this has relied on shifting the pitch of the light based on how many particles are present, a bit like how a guitar string changes tone when you press down on it. But this method has limits; it treats the light as a passive object that only shifts its frequency, rather than something that can actively change how strongly it interacts with the rest of the machine.

A team of researchers has now discovered a way to go much deeper, finding a method where the number of particles in one part of the circuit directly controls how strongly a specific interaction happens in another part, without changing the number of particles in the first place. Imagine a musician playing a note on a piano while a second musician, sitting nearby, holds a single key down. In this new setup, the second musician's action doesn't just change the pitch of the first note; it actually changes how loudly or softly the first musician can play a specific chord. This is not just a subtle shift in tone; it is a fundamental change in the strength of the connection between the two. By using a special superconducting loop called a SQUID, which acts as a tunable bridge for electricity, the researchers modeled a system where the presence of photons in a "controller" mode reshapes the very rules of engagement for a "signal" mode.

The researchers analyzed a circuit where two different vibrating modes of electricity share the same physical bridge. They pumped this bridge with a rhythmic magnetic signal, a technique known as flux pumping, which is designed to create pairs of photons in the signal mode. Usually, when scientists want to control such a process, they rely on the fact that the presence of other particles shifts the frequency of the interaction. If the controller has zero particles, the signal resonates at one frequency; if it has one, it resonates at another. This is a well-known effect called a cross-Kerr shift. However, the team found that this frequency shift was only half the story. Even after they carefully tuned the system so that the signal was perfectly in resonance for every different number of controller particles, the strength of the interaction—the size of the gap between energy levels—still changed depending on how many particles were in the controller.

To understand this, the researchers had to look at the raw mathematics of the superconducting loop, which behaves like a wave that can be described by a cosine function. When they calculated the exact probability of creating a pair of photons in the signal mode while leaving the controller mode untouched, they found that the controller's particle count appeared directly in the formula. It was as if the controller was whispering a secret to the interaction, altering its volume without ever speaking a word itself. This effect arises because the quantum fluctuations of the controller mode are physically present in the same nonlinear element as the signal mode. Even though no energy is exchanged between them during the specific transition, the mere existence of the controller's particles modifies the landscape through which the signal travels.

The team verified this discovery through a combination of advanced mathematical modeling and high-precision numerical simulations. They compared their simplified theories against a full, unexpanded simulation of the circuit, which acts as a perfect reference. The results showed that the interaction strength varied significantly across the different possible states of the controller. For instance, when the controller was empty, the interaction had one specific strength. When the controller held just one particle, the strength dropped noticeably. This variation was not a side effect of the frequency shift; it was a distinct, measurable property of the interaction itself. By mapping out these changes, the researchers created a two-dimensional landscape where both the pitch and the volume of the interaction could be controlled independently by the state of the controller.

This control opens up new possibilities for how quantum information can be processed. Because the interaction strength depends on the controller's state, the researchers could selectively drive a specific transition within the signal mode while ignoring others. They demonstrated that by tuning the pump frequency to a specific spot, they could move the signal from having two particles to having four, with high precision, while leaving other potential transitions untouched. This selectivity is crucial for building complex quantum memories, where one needs to address a single piece of data without accidentally disturbing its neighbors. The researchers found that they could trade off speed for precision; by using a weaker pump, they could make the selection even sharper, though it would take longer to complete the operation.

Beyond simple selection, the researchers explored what happens when the controller is placed in a quantum superposition, a state where it effectively holds two different numbers of particles at once. In this scenario, the signal mode does not just follow one path; it follows two different paths simultaneously, each dictated by a different state of the controller. Because the interaction strength and resonance are different for each path, the signal evolves in two distinct ways at the same time. This creates a deep connection, or entanglement, between the controller and the signal. The researchers calculated that this process could generate nearly one full unit of entanglement, a significant amount for quantum systems, effectively linking the state of the controller to the state of the signal in a way that cannot be described by classical physics.

Furthermore, the team showed that this mechanism could be used to create highly complex, non-standard quantum states. When the signal is driven in a specific controller sector, it climbs a ladder of energy levels in a way that distorts its shape, creating regions of negative probability in its quantum map. These "negative" regions are a hallmark of truly quantum behavior that cannot be mimicked by simple waves. The researchers found that by choosing the right controller state, they could force the signal into this highly non-classical regime, while leaving signals in other controller states almost completely unaffected. This ability to turn on complex quantum dynamics with a simple switch of the controller's state offers a powerful new tool for generating the exotic states needed for advanced quantum error correction and sensing.

The findings were not just theoretical; the researchers provided a clear roadmap for how this could be built in a real laboratory. They identified the specific conditions required to isolate this effect from other noisy signals that might interfere in a real circuit. By ensuring that the frequencies of other unwanted modes are far enough away from the pump signal, the desired interaction can be made to stand out clearly. The team confirmed that the necessary components, such as the superconducting loops and the ability to tune them with magnetic fields, are already available in modern quantum computing hardware. This means that the occupation-controlled interaction is not a distant dream but a feature that can be engineered into existing devices.

In the end, this work reveals a new layer of control in the quantum world. It shows that the state of one part of a system can do more than just shift the frequency of another part; it can fundamentally alter the strength of their connection. This discovery moves beyond the idea of simple frequency tuning and introduces a method where the very nature of the interaction is conditional on the quantum state of a partner. By mastering this conditional dynamics, scientists can build more precise, more selective, and more powerful quantum machines, capable of manipulating light in ways that were previously thought impossible. The ability to generate entanglement and complex quantum states on demand, simply by preparing a controller in the right state, marks a significant step forward in the practical engineering of quantum technologies.